Learn how to compose two linear functions. To compose two functions means to express one of the functions as a function of the other function. This is done by replacing the input variable of one of ...

Abstract: In environmental modeling, the impact of fixed scatterers on the background environment can be effectively accounted for by using numerical Green's functions (NGF), which significantly ...

Abstract: This paper studies the control-oriented recursive identification of finite impulse response systems with binary-valued observations. Inspired by the Maximum Likelihood method, a novel ...

Over 21 days of talking with ChatGPT, an otherwise perfectly sane man became convinced that he was a real-life superhero. We analyzed the conversation. By Kashmir Hill and Dylan Freedman Kashmir Hill ...

After finding the homeschooling life confining, the teen petitioned her way into a graduate class at Berkeley, where she ended up disproving a 40-year-old conjecture. It’s not that anyone ever said ...

Copyright © William D. Young. All rights reserved. Recursion is a very useful programming skill. You may not use it very often in most languages, but the ability to ...

This film discusses the concept of functions in mathematics, emphasizing their importance and modern formulations. It explains how to create ordered pairs from a set of numbers and illustrates how ...

ABSTRACT: For decades, Lychrel numbers have been studied on many bases. Their existence has been proven in base 2, 11 or 17. This paper presents a probabilistic proof of the existence of Lychrel ...